Identification of the governing equation of stimulus-response data for run-and-tumble dynamics

The run-and-tumble behavior is a simple yet powerful mechanism that enables microorganisms to efficiently navigate and adapt to their environment. These organisms run and tumble alternately, with transition rates modulated by intracellular chemical concentration. We introduce a neural network-based model capable of identifying the governing equations underlying run-and-tumble dynamics. This model accommodates the nonlinear functions describing movement responses to intracellular biochemical reactions by integrating the general structure of ODEs that represent these reactions, without requiring explicit reconstruction of the reaction mechanisms. It is trained on datasets of measured responses to simple, controllable signals. The resulting model is capable of predicting movement responses in more realistic, complex, temporally varying environments. Moreover, the model can be used to deduce the underlying structure of hidden intracellular biochemical dynamics. We have successfully tested the validity of the identified equations based on various models of Escherichia coli chemotaxis, demonstrating efficacy even in the presence of noisy measurements. Moreover, we have identified the governing equation of the photo-response of Euglena gracilis cells using experimental data, which was previously unknown, and predicted the potential architecture of the intracellular photo-response pathways for these cells.Author summary: Microscopic organisms like bacteria and algae often adjust their movement in response to changing environments, such as light or chemical signals. They do this using a behavior called run-and-tumble, alternating between straight swimming and reorientation. Understanding how internal cell processes drive this behavior is difficult, especially when we can’t directly observe the biochemical pathways involved. In this study, we present a machine learning approach that discovers the governing rules behind these behaviors using only observable input-output data. Our model, based on neural networks, learns from how cells respond to simple stimuli and can predict how they behave under more complex, realistic conditions, without needing to know the details of internal reactions. We validated the method using simulations of bacterial chemotaxis and real experimental data from Euglena gracilis, a microorganism that responds to light. Our model accurately predicted cell responses and revealed insights into possible internal signaling structures. This approach provides a powerful tool for studying biological behavior and could help uncover how other organisms process environmental information.